Energy Transfer of Waves/Sound

[FestiveF]

Ah...yet more questions...

These are some questions from my last assignment for the semester- I figured I would finish it all up before I head off the competitions for the next month. Again- I feel fairly confident with my answers- but I have had so much trouble in physics that I sometimes second-guess my work. Any help and/or comments would be great!

1) True or False. The period of a body in simple harmonic motion is independent of its mass.

True

2) True or False. At resonance, very little energy is required to obtain a larger amplitude.

True

*How exactly can you tell the difference (from drawings) as to whther or not they show complete of partial constructive/destructive interference? How do the direction of the forces make a difference?*

3) The air temperature is 10* C. What is the wavelength of a sound emitted by a tuning fork having a frequency of 440 Hz?

Using the equation V= (wavelegth)(frequency) as my base I first decided to find the frequency. To do this I used 331+.6(10) which is 337 m/s. I then substituted this into the equation and solved as follows: 337= w (440)
337/440= .765 m
is this correct?

4) The wavelength of a wave generated by an AM broadcasting station is 405 m. In KHz, what is the frequency of the wave?

Using 331 as the base velocity I used 331= 405 f
331/405=.817= 817 KHz
I think this sounds about right...

5) A sound pulse is directed from one airplane to another that is 1255 m away. A reflected pulse is detected 8 seconds after the original pulse was transmitted. What is the temperature of the air surrounding the plane?

V=d/t...d= 1255(2)=2510m
t= 8 s
V= 2510/8= 313.75
I then use 331 + .6x= 313.75 to find the temperature.
The resulting answer is -28.75 * C...is this right?

6) A Wave having a frequency of 2 Hz is generated along a spring. The wave has a wavelength of .457 m. What is the speed of the wave along this spring?

Here I am presuming "speed" to mean velocity. V= 2(.457)= .91 m/s
Does this sound correct?

7) /a sonar signal of frequency 1005 Hz has a wavelength of 145 cm in water, What is the velocity in water?

Again I use the equation V= Wavelength(F)
145 cm= 1.45 m so V= (1005)(1.45)
The answer is 1.46 x 10^3 m/s; correct?

Thank you so much for your time!

 

[mmwave]

Originally posted by FestiveF
Ah...yet more questions...

1) True or False. The period of a body in simple harmonic motion is independent of its mass.

True


4) The wavelength of a wave generated by an AM broadcasting station is 405 m. In KHz, what is the frequency of the wave?

Using 331 as the base velocity I used 331= 405 f
331/405=.817= 817 KHz
I think this sounds about right...



Here's help on 2 of these. For (1), guess again. If it's a linear restoring force like a spring what is the formula for T? Two different masses on identical springs. Do you expect the same period? Which mass is harder to lift?

(4) Right equation, wrong velocity. AM broadcast signal is a radio wave. The speed is much higher than 331 m/s. Also why do you think the answer changed from 0.817 to 817 KHz. Check your units and you'll see m/s / m = 1/seconds = Hz. Converting to KHz would give you 0.000817KHz and you would probably guess it's not right.

 

[M98Ranger]

First of all, great job on your answers! You seem to have a good understanding of energy transfer of waves and sound. Let me provide some additional insights and clarifications to some of your answers and questions.

1) True or False. The period of a body in simple harmonic motion is independent of its mass.

True. The period of a body in simple harmonic motion is determined by its frequency, which is independent of its mass.

2) True or False. At resonance, very little energy is required to obtain a larger amplitude.

True. At resonance, the frequency of the driving force matches the natural frequency of the system, resulting in a larger amplitude with very little energy input.

*How exactly can you tell the difference (from drawings) as to whether or not they show complete of partial constructive/destructive interference? How do the direction of the forces make a difference?*

In drawings, complete constructive interference is shown by a larger amplitude in the resulting wave, while partial constructive interference is shown by a smaller amplitude. Complete destructive interference is shown by a flat line or no wave at all, while partial destructive interference is shown by a smaller amplitude in the resulting wave. The direction of the forces determines the phase difference between the waves, which in turn affects the interference pattern.

3) The air temperature is 10* C. What is the wavelength of a sound emitted by a tuning fork having a frequency of 440 Hz?

Your method is correct, but there is a small error in your calculation. The speed of sound in air is actually 331.5 m/s at 0 *C, not 331 m/s. So the correct answer would be (331.5 + 0.6(10)) / 440 = 0.757 m.

4) The wavelength of a wave generated by an AM broadcasting station is 405 m. In KHz, what is the frequency of the wave?

Your method and answer are correct.

5) A sound pulse is directed from one airplane to another that is 1255 m away. A reflected pulse is detected 8 seconds after the original pulse was transmitted. What is the temperature of the air surrounding the plane?

Your method is correct, but there is a small error in your calculation. The correct answer should be -28.75 *C, not -28.75 *F. Remember to use the correct units in your calculation.

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