# Sound Questions (Waves)

1. 1) The intensity of a sound is 1.0*10-7 W/m^2. Determine the intensity level of the sound in decibels.

By definition the dB intensity of a sound having an intensity I is

$dB = 10*log(I/I0), where I0 =10^{-12} W/m^2$

$10*log(10^{-7}/10^{-12})=10*log(10^5) =50 dB$

2. The intensity of the sound produced by a violin at a distance of 10 m is 1.0*10{-4} W/m^2. Determine the intensity level of the sound in decibels.

Same considerations as before

$10*log(10^{-4}/10^{-12}) =10*log(10^8) =8*10=80 dB$

3. The intensity level of the sound from a jet plane at a distance of 30 m is 140 dB. Determine the intensity of the sound.

Same considerations as at point 1.

$140=10*log(I/10^{-12})$

$log(I*10^{12}) =14$

$10^{14} =I*10^{12}$

$I= 100 W/m^2$

4.  During a classroom lecture, the intensity level of the instructor’s voice is approximately 60 dB. Determine the intensity of this sound in W/m^2

Same considerations as at point 1

$60 = 10*log(I/10^{-12})$

$log(I*10^{12}) =6$

$I*10^{12}=10^6$

$I =10^{-6} W/m^2$

5. What is the length of a pipe open at both ends second harmonic frequency produced by the pipe is 340 Hz. Assume that the speed of sound is 340 m/s.

There are maximum of standing waves at both ends of pipe (they are open). Hence inside the pipe the first harmonic has $\lambda/2$  ($\lambda$ is the wavelength) and the second harmonic has $\lambda$ (an entire wavelength)

speed of sound is $v =340 m/s$

$T (period) = 1/F$ , $F$ is the frequency

$\lambda = T*v =v/F =340/340 = 1 m$

Hence the length of the pipe should be 1 m.

6. A pipe closed at at one end is 1.0 m long. What is the frequency of the first harmonic produced by the pipe. Assume that the speed of sound is 340 m/s.

The pipe has at the open end a maximum of standing wave and at closed end a minimum of standing wave. Hence the length inside the pipe is $\lambda/4$.

$\lambda/4 =1$

$\lambda = 4 m$

$\lambda = v/F$

$F = v/\lambda =340/4 = 85 Hz$

7. The predominant frequency produced by a certain police car’s siren is 2000 Hz. The police car is moving TOWARD a stationary observer at 40.0 m/s. If the speed of sound in air is 340 m/s. Determine the frequency detected by the observer.

The formula for the Doppler effect is

$F = (c+Vr)/(c+Vs)*F0$

where F is the frequency heard, F0 is the initial frequency

c is the speed of sound

Vr is the speed of the receiver (positive is the receiver is moving towards the source)

Vs is the speed of the source (positive if the source is moving away from receiver)

F0=2000 Hz, c =340 m/s, Vr = 0 m/s, vs =-40 m/s

$F =(340/(340-40))*2000 =2266.7 Hz$

8. The predominant frequency produced by a certain police car’s siren is 2000 Hz. The police car is moving AWAY from a stationary observer at 40.0 m/s. I f the speed of sound in air is 340 m/s. Determine the frequency detected by the observer.

Same considerations as at point 7.

F0 =2000 Hz, c =340 m/s, Vr =0 m/s, Vs=+40 m/s

$F =(340/(340+40))*2000 =1789.47 m/s$

9.  The predominant frequency produced by a certain stationary police car’s siren is 2000 Hz. An observer is approaching the stationary police car at 40.0 m/s. If the speed of sound in air is 340 m/s. Determine the frequency detected by the observer.

Same considerations as at point 7.

F0 =2000 Hz, c =340 m/s, Vr =+40 m/s, Vs =0 m/s

$F = ((340+40)/340)*2000=2235.3 m/s$

10. Same considerations as at point 7.

F0=2000 Hz, c =340 m/s, vr =-40 m/s, vs =0 m/s

$F= ((340-40)/340))*2000 =1764.7 Hz$

11. As a classroom demonstration of the Doppler effect, a teacher whirls a child’s toy in a horizontal circle of radius 1.00 m with the frequency of revolution is 60.0 rpm. As the toy revolves it makes a whistling sound of frequency 200 Hz. Determine the maximum and minimum frequencies heard by students who are sitting at some distance from the teacher. Assume that the speed of sound is 340 m/s.

speed of toy $= \omega*r = (2*\pi*F)*r = 2*\pi*(60/60)*1=6.28 m/s$

F is the frequency of the rotation of the toy

maximum frequency of sound heard is

$F = (340/(340-6.28))*200 =203.76 Hz$

minimum frequency of sound heard

$F =(340/(340+6.28))*200 =196.37 Hz$

12. A train and a car are approaching each other. The train is travelling at 40.0 m/s while the car’s speed is 30.0 m/s. The frequency of the train whistle is 1000 Hz. Assuming the speed of sound is 340 m/s. Determine the frequency heard by the driver of the car.

Same considerations as at point 7.

F0 =1000 Hz, c =340 m/s, Vr =+30 m/s, Vs =-40 m/s

$F =((340+30)/(340-40))*1000 =1233.3 Hz$