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Practice Homework 13 - practice 13 ALIBHAI ZAHID Latest...

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practice 13 – ALIBHAI, ZAHID 1 Latest unpenalized work: Apr 22 2007 Sunday 04:00 (after this date you can not make a perfect score). Work cutoff: Apr 22 2007, 4:00 am. Question 1 part 1 of 3 10 points Two waves in one string are described by the relationships y 1 = A 1 cos( k 1 x - ω 1 t ) y 2 = A 2 sin( k 2 x - ω 2 t ) where A 1 = 2 . 2 cm, A 2 = 2 . 7 cm, k 1 = 6 cm 1 , k 2 = 4 cm 1 , ω 1 = 3 rad / s, ω 2 = 4 rad / s, y and x are in centimeters, and t is in seconds. Find the superposition of the waves y 1 + y 2 at the position x 1 = 0 . 5 cm and time t 1 = 2 s. Answer in units of cm. Question 2 part 2 of 3 10 points Find the superposition of the waves y 1 + y 2 at the position x 2 = 1 cm and time t 2 = 0 . 7 s. Answer in units of cm. Question 3 part 3 of 3 10 points Find the superposition of the waves y 1 + y 2 at the position x 3 = 0 . 5 cm and time t 3 = - 0 . 38 s. Answer in units of cm. Question 4 part 1 of 2 10 points Two sound sources radiating in phase at a frequency of 540 Hz interfere such that max- ima are heard at angles of 0 and 24 from a line perpendicular to that joining the two sources. The velocity of sound is 340 m/s. y L d S 1 S 2 θ listening direction θ δ Find the separation between the two sources. Answer in units of m. Question 5 part 2 of 2 10 points Find the next larger angle at which a max- imum intensity will be heard. Answer in units of . Question 6 part 1 of 1 10 points A light string of mass per unit length 8 . 62 g / m has its ends tied to two walls sepa- rated by a distance equal to three fourths the length L of the string as shown in the figure. A mass m is suspended from the center of the string, applying a tension in the string. The acceleration of gravity is 9 . 8 m / s 2 . 3 L 4 m g L 2 L 2 θ θ What size mass should be suspended from the string to produce a wave speed of 88 . 9 m / s? Answer in units of kg. Question 7
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practice 13 – ALIBHAI, ZAHID 2 part 1 of 1 10 points An incident sine wave y i ( x, t ) = A sin( k x - ω t ) (1) travels to the right and is reflected off a fixed end of the string at x = L . Which of the following expression gives the correct formula for the reflected wave y r ( x, t )? 1. y r ( x, t ) = A sin( k x + ω t + 2 k L ) 2. y r ( x, t ) = A sin( k x + ω t ) 3. y r ( x, t ) = A sin( k x + ω t - k L ) 4. y r ( x, t ) = A sin( k x - ω t + 2 k L ) 5. y r ( x, t ) = A sin( k x - ω t ) 6. y r ( x, t ) = A sin( k x + ω t - 2 k L ) 7. y r ( x, t ) = A sin( k x - ω t - 2 k L ) 8. y r ( x, t ) = A sin( k x + ω t + k L ) 9. y r ( x, t ) = A sin( k x - ω t + k L ) 10. y r ( x, t ) = A sin( k x - ω t - k L ) Question 8 part 1 of 1 10 points You are given f 1 ( x ), a transverse wave that moves on a string that ends and is FIXED in place at x = 5 m. As the problem begins, the wave is moving to the right at v = 1 m/s. v 0 1 2 3 4 5 -3 -2 -1 0 1 2 3 Amplitude (centimeter) Distance (meter) What is the shape of the wave on the string after 5 s? 1. 0 1 2 3 4 5 -3 -2 -1 0 1 2 3 Distance (meter) 2. 0 1 2 3 4 5 -3 -2 -1 0 1 2 3 Distance (meter) 3. 0
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