1 . A sound source emits sounds of frequency 195 Hz that travel through still ai

Question

1. A sound source emits sounds of frequency 195 Hz that travel through still air at 340 m/s. The listener moves at 80 m/s relative to still air toward the stationary source. What is the wavelength of the sound between the source and the listener?

2. A bystander hears a siren vary in frequency from 570 Hz to 389 Hz as a fire truck approaches, passes by, and moves away on a straight street. What is the speed of the truck? (Take the speed of sound in air to be 343 m/s.)

6. What is the beat frequency heard when two organ pipes, each open at both ends, are sounded together at their fundamental frequencies if one pipe is 48 cm long and the other is 61 cm long?(The speed of sound is 340 m/s)

10. A guitar string is 98 cm long and has a mass of 3.2 g. From the bridge to the support post (L) is 65 cm, and the string is under a tension of 540 N. What is the frequency of the first overtone?

Explanation / Answer

1.

frequency heard By the observer

f =f *(V+Vo/V) =195*(340+80/340)

f=240.88 Hz

wave length of sound is

lambda =V/f =340/240.88

lambda =1.41 m

2.

f_H =fo*(V/V-Vs)

570 =fo*(V/V-Vs)

fo =570*(V-Vs/V)----1

f_L = 389=fo*(V/V+Vs)

fo =389*(V+Vs/V)---2

1=2

389*(V+Vs/V) =570*(V-Vs/V)

389V+389Vs =570V-570Vs

959Vs =181V

959*Vs =181*343

Vs=64.74 m/s

6.

lambda 1=2L1 =2*0.48 =0.96 m

f1=V/lambda1 =340/0.96 =354.17 Hz

lambda2 =2L2=2*0.61=1.22 m

f2 =V/lmbda2=340/1.22 =278.69 Hz

therefore beat frequency is

dF =f1-f2 =75.5 Hz

10.

linear mass density

u=m/L =(3.2*10^-3/0.98)=3.2653*10^-3 Kg/m

V=sqrt(T/u) =sqrt(540/3.2653*10^-3)

V=406.66 m/s

At the fundamental, the string has two nodes at the end, and one anti-node in the middle, so therefore the vibrating length of the string

L=lambda/2

lambda =2L =2*0.65 =1.3 m

f =V/lambda =406.66/1.3 =312.82

fundmental frequency

f1 =f =312.82 Hz

f2=2f1 =625.64 Hz (first overtone)

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