Select the correct answer 10. Two harmonic waves traveling in opposite direction

Question

Select the correct answer

10.   Two harmonic waves traveling in opposite directions interfere to produce a standing wave described by y= 4 sin (5x) cos (6t) where xis in m and tis in s. What is the approximate frequency of the interfering waves?

a.

3 Hz

b.

1 Hz

c.

6 Hz

d.

12 Hz

e.

5 Hz

           

   11.   A string is stretched and fixed at both ends, 200 cm apart. If the density of the string is 0.015 g/cm, and its tension is 600 N, what is the fundamental frequency?

a.

316 Hz

b.

632 Hz

c.

158 Hz

d.

215 Hz

e.

79 Hz

   12.   Two tuning forks with frequencies 264 and 262 Hz produce "beats". What is the beat frequency (in Hz)?

a.

4

b.

2

c.

1

d.

3

e.

0 (no beats are produced)

           

   13.   Two instruments produce a beat frequency of 5 Hz. If one has a frequency of 264 Hz, what could be the frequency of the other instrument?

a.

269 Hz

b.

254 Hz

c.

264 Hz

d.

5 Hz

e.

274 Hz

a.

3 Hz

b.

1 Hz

c.

6 Hz

d.

12 Hz

e.

5 Hz

Explanation / Answer

1)

y = 4 sin (5x) cos (6t) where k = 5 rad/m, omega = 6 rad/s

Frequency, f = omega/2pi = 6/ 2 pi = 0.955 Hz ~ 1 Hz

2)

the fundamental frequency is nf = 1 / 2L x sqrt ( T / m )

= ( 1/2 x2 ) sqrt( 600/15x10^-4) = 50 x sqrt (10) / 4 = 158 Hz

3)

f beat = f1 - f2 = 264 - 262 = 2 Hz

4)

Frequency, f2 = 264+5 = 269 Hz

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