{"id":3340,"date":"2018-07-08T14:24:49","date_gmt":"2018-07-08T21:24:49","guid":{"rendered":"https:\/\/gurumuda.net\/physics\/?p=3340"},"modified":"2018-07-08T14:24:49","modified_gmt":"2018-07-08T21:24:49","slug":"transverse-waves-problems-and-solutions","status":"publish","type":"post","link":"https:\/\/gurumuda.net\/physics\/transverse-waves-problems-and-solutions.htm","title":{"rendered":"Transverse waves – problems and solutions","gt_translate_keys":[{"key":"rendered","format":"text"}]},"content":{"rendered":"

1. The distance<\/a> between the two troughs of the water surface waves is 20 m. An object floats on the surface of the water so that it experiences the vibration motion. If the time to travel one vibration is 4 seconds, then the velocity of the wave is \u2026. m\/s<\/span><\/span><\/p>\n

A. 20 <\/span><\/span><\/p>\n

B. 15<\/span><\/span><\/p>\n

C. 10<\/span><\/span><\/p>\n

D. 5<\/span><\/span><\/p>\n

Known :<\/u><\/span><\/span><\/p>\n

Wavelength<\/a> (\u03bb) = 20 meters<\/span><\/span><\/p>\n

Period (T) = 4 seconds<\/span><\/span><\/p>\n

Wanted:<\/u><\/span><\/span> Speed of wave (v)<\/span><\/span><\/p>\n

Solution :<\/u><\/span><\/span><\/p>\n

The equation of the speed of wave :<\/span><\/span><\/p>\n

v = \u03bb \/ T = 20 meters \/ 4 seconds = 5 meters \/ second<\/span><\/span><\/p>\n

The correct answer is D.<\/span><\/span><\/p>\n

2. <\/span><\/span>Two points A and B are on the rope and are 90 cm apart from one another. On the rope propagates the transverse waves<\/a>, so that point A is at the top of the wave, point B at the bottom of the wave, and between them, there are two crests and two troughs. If the wave period is 0.3 seconds, then the wave propagation is\u2026<\/span><\/span><\/span><\/p>\n

A. 10.8 cm\/s<\/span><\/span><\/p>\n

B. 18.0 cm\/s<\/span><\/span><\/p>\n

C. 120.0 cm\/s<\/span><\/span><\/p>\n

D. 200.0 cm\/s<\/span><\/span><\/p>\n

Known :<\/u><\/span><\/span><\/p>\n

Distance AB (l) = 90 cm <\/span><\/span><\/p>\n

Period of wave (T) = 0.3 seconds<\/span><\/span><\/p>\n

Frequency of wave (f) = 1\/0.3 seconds<\/span><\/span><\/p>\n

Point A is at the crest of the wave and point B is at the trough of the wave.<\/span><\/span><\/p>\n

Between point A and B, there are two crests and two troughs.<\/span><\/span><\/p>\n

Wanted :<\/u><\/span><\/span> Speed of wave (v = f \u03bb)<\/span><\/span><\/p>\n

Solution :<\/u><\/span><\/span><\/p>\n

\"TransverseBased on figure, can conclude there are 2.5 wavelengths. Distance of a wavelength (\u03bb) = 90 cm \/ 2.5 = 36 cm <\/span><\/span><\/p>\n

The speed of wave :<\/span><\/span><\/p>\n

v = f \u03bb = (1 \/ 0.3)(36) = 36 \/ 0.3 = 120 cm\/s.<\/span><\/span><\/p>\n

The correct answer is C.<\/span><\/span><\/p>\n

3. <\/span><\/span>The following graph displays the displacement of a point in one medium as a function of time when a wave passes through the medium.<\/span><\/span><\/span><\/p>\n

\"Transverse<\/p>\n

If the wavelength is 6 meters, then the speed of the wave propagation is\u2026<\/span><\/span><\/span><\/p>\n

A. 3 m\/s<\/span><\/span><\/p>\n

B. 6 m\/s<\/span><\/span><\/p>\n

C. 8 m\/s<\/span><\/span><\/p>\n

D. 12 m\/s<\/span><\/span><\/p>\n

Known :<\/u><\/span><\/span><\/p>\n

There are two wavelengths based on the graph above.<\/span><\/span><\/p>\n

Distance of 1 wavelength (\u03bb) = 6 meters \/ 2 = 3 meters<\/span><\/span><\/p>\n

Period (T) = 0.5 seconds<\/span><\/span><\/p>\n

Wanted :<\/u><\/span><\/span> Speed of waves (v)<\/span><\/span><\/p>\n

Solution :<\/u><\/span><\/span><\/p>\n

v = f \u03bb = \u03bb \/ T = 3 meters \/ 0.5 seconds = 6 meters \/ second<\/span><\/span><\/p>\n

The correct answer is B.<\/span><\/span><\/p>\n

4. Based on the figure below, t<\/span><\/span>he point that has phase difference \u00be with point A is \u2026.<\/span><\/span><\/span><\/p>\n

A. Point B\"Transverse<\/span><\/span><\/p>\n

B. Point C<\/span><\/span><\/p>\n

C. Point D<\/span><\/span><\/p>\n

D. Point E<\/span><\/span><\/p>\n

Solution<\/span><\/span><\/p>\n

\n

Point B has a phase difference of \u00bc \u03bb with point A
\nPoint C has a phase difference of 2\/4 \u03bb or 1\/2 \u03bb with point A
\nPoint D has a phase difference of 3\/4 \u03bb with point A
\nPoint F has a phase difference of 5\/4 \u03bb with point A.
\nThe correct answer is C.<\/span><\/span><\/span><\/p>\n

5. <\/span><\/span>On a pond’s surface, there are two dry leaves 60 centimeters away from each other. Both move up and down like the surface of the water with a frequency of 2 Hz. When one leaf is at the crest, the other leaves are at the trough, and between them, there is one crest and one trough. Determine the speed of the wave propagation of the wave.<\/span><\/span><\/span><\/p>\n<\/div>\n

A. 20 cm\/s<\/span><\/span><\/p>\n

B. 30 cm\/s<\/span><\/span><\/p>\n

C. 80 cm\/s<\/span><\/span><\/p>\n

D. 120 cm\/s<\/span><\/span><\/p>\n

Known :<\/u><\/span><\/span><\/p>\n

Distance between both leaves = 60 cm<\/span><\/span><\/p>\n

Frequency (f) = 2 Hz = 2<\/span><\/span><\/p>\n

Wanted :<\/u><\/span><\/span> The speed of wave<\/span><\/span><\/p>\n

Solution :<\/u><\/span><\/span><\/p>\n

\"TransverseBetween both leaves, there are 1.5 wavelengths. Distance of 1 wavelength is (\u03bb) = 60 cm \/ 1.5 = 40 cm<\/span><\/span><\/p>\n

Speed of wave (v) :<\/span><\/span><\/p>\n

v = f \u03bb = (2 Hz)(40 cm) = 80 cm\/second<\/span><\/span><\/p>\n

The correct answer is C.<\/span><\/span><\/p>\n

6. Based on the figure below, determine the amplitude, period, frequency, and speed of the wave.<\/span><\/span><\/p>\n

\"Transverse<\/p>\n

Solution :<\/span><\/span><\/p>\n

Amplitude (A) = 4 meters<\/span><\/span><\/p>\n

Period (T) = 6 seconds \/ 3 = 2 seconds<\/span><\/span><\/p>\n

Frequency (f) = 1 \/ T = 1 \/ 2 = 0.5 hertz <\/span><\/span><\/p>\n

Wavelength (\u03bb) = 24 meters \/ 3 = 8 meters<\/span><\/span><\/p>\n

Speed of wave (v) = f \u03bb = (0.5 hertz)(8 meters) = 4 meters\/second or<\/span><\/span><\/p>\n

Speed of wave (v) = \u03bb \/ T = 8 meters \/ 2 second = 4 meters\/second<\/span><\/span><\/p>\n

The correct answer is D. <\/span><\/span><\/p>\n

7. <\/span><\/span>On a string with length of 1.2 m and mass of 200 g formed 1.5 sinusoidal waves with frequency of 50 Hz. Based on these data, determine the wave period and the tension force of the rope.<\/span><\/span><\/span><\/p>\n

A. Period = 0.02 seconds and tension force = 6.67 N<\/span><\/span><\/p>\n

B. Period = 0.01 seconds and tension force = 6.67 N<\/span><\/span><\/p>\n

C. Period = 0.02 seconds and tension force = 266.67 N<\/span><\/span><\/p>\n

D. Period = 0.01 seconds and tension force = 266.67 N<\/span><\/span><\/p>\n

Known :<\/u><\/span><\/span><\/p>\n

Length of rope (l) = 1.2 meters and there are 1.5 sinusoidal waves so that distance of 1 wavelength (\u03bb) = 1.2 meters \/ 1.5 = 0.8 meters <\/span><\/span><\/p>\n

Mass of rope (m) = 200 gram = 0.2 kg<\/span><\/span><\/p>\n

Frequency (f) = 50 Hz<\/span><\/span><\/p>\n

Density of rope (\u00b5) = m\/l = 0.2 kg \/ 1.2 meters = (1\/6) kg\/meter<\/span><\/span><\/p>\n

Wanted :<\/u><\/span><\/span> Period of wave (T) and the tension force of rope (T)<\/span><\/span><\/p>\n

Solution :<\/u><\/span><\/span><\/p>\n

Period of wave :<\/span><\/span><\/p>\n

T = 1 \/ f = 1 \/ 50 Hz = 0.02 seconds<\/span><\/span><\/p>\n

The speed of wave on rope :<\/span><\/span><\/p>\n

v = f \u03bb = (50 Hz)(0.8 meters) = 40 meters\/second<\/span><\/span><\/p>\n

The tension force (T) :<\/span><\/span><\/p>\n

\"Transverse<\/p>\n

The correct answer is C.<\/span><\/span><\/p>\n","protected":false,"gt_translate_keys":[{"key":"rendered","format":"html"}]},"excerpt":{"rendered":"

1. The distance between the two troughs of the water surface waves is 20 m. An object floats on the surface of the water so that it experiences the vibration motion. If the time to travel one vibration is 4 seconds, then the velocity of the wave is \u2026. m\/s A. 20 B. 15 C. … Read more<\/a><\/p>\n","protected":false,"gt_translate_keys":[{"key":"rendered","format":"html"}]},"author":1,"featured_media":0,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"_seopress_titles_title":"","_seopress_titles_desc":"","_seopress_robots_index":"","_seopress_robots_follow":"","_seopress_robots_imageindex":"","_seopress_robots_snippet":"","_seopress_robots_primary_cat":"","_seopress_robots_breadcrumbs":"","_seopress_robots_freeze_modified_date":"","_seopress_robots_custom_modified_date":"","_seopress_robots_canonical":"","_seopress_social_fb_title":"","_seopress_social_fb_desc":"","_seopress_social_fb_img":"","_seopress_social_fb_img_attachment_id":0,"_seopress_social_fb_img_width":0,"_seopress_social_fb_img_height":0,"_seopress_social_twitter_title":"","_seopress_social_twitter_desc":"","_seopress_social_twitter_img":"","_seopress_social_twitter_img_attachment_id":0,"_seopress_social_twitter_img_width":0,"_seopress_social_twitter_img_height":0,"_seopress_redirections_value":"","_seopress_redirections_enabled":"","_seopress_redirections_enabled_regex":"","_seopress_redirections_logged_status":"","_seopress_redirections_param":"","_seopress_redirections_type":0,"_seopress_analysis_target_kw":"Transverse waves - problems and solutions","_seopress_news_disabled":"","_seopress_video_disabled":"","_seopress_video":[],"_seopress_pro_schemas_manual":[],"_seopress_pro_rich_snippets_disable_all":"","_seopress_pro_rich_snippets_disable":[],"_seopress_pro_schemas":[],"footnotes":""},"categories":[3],"tags":[],"class_list":["post-3340","post","type-post","status-publish","format-standard","hentry","category-solved-problems-in-basic-physics"],"gt_translate_keys":[{"key":"link","format":"url"}],"_links":{"self":[{"href":"https:\/\/gurumuda.net\/physics\/wp-json\/wp\/v2\/posts\/3340","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/gurumuda.net\/physics\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/gurumuda.net\/physics\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/gurumuda.net\/physics\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/gurumuda.net\/physics\/wp-json\/wp\/v2\/comments?post=3340"}],"version-history":[{"count":0,"href":"https:\/\/gurumuda.net\/physics\/wp-json\/wp\/v2\/posts\/3340\/revisions"}],"wp:attachment":[{"href":"https:\/\/gurumuda.net\/physics\/wp-json\/wp\/v2\/media?parent=3340"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/gurumuda.net\/physics\/wp-json\/wp\/v2\/categories?post=3340"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/gurumuda.net\/physics\/wp-json\/wp\/v2\/tags?post=3340"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}