Physics: waves and sound help

[pakman127]

Homework Statement

1) A boy sitting on a dock notices that in 4.0 min, 36 wave crests pass by him. Determine the frequency and period of the water waves.

2) A string of length 2.0m is stretched between two fixed ends. When the string vibrates with a frequency of 60Hz, you notice six nodes (including the ends):

a) Which harmonic is this?

b) Determine the speed of the wave in the string

c) Determine the frequency of the fundamental node in this string

3) Two brains have identical whistles that emit a sound at 220Hz. Train A moves away from Train B at some constant speed. A woman at rest on Train B notes that while Train A is moving, the combination of the two whistles results in a beat frequency of 6.0Hz. The speed of sound in the air is 330m/s.

a) What frequency does the woman hear from the whistle of Train A?

b) What is the speed of train A?

Homework Equations

f= 1/T
v=f × λ
fn=nv/2L
λ-n = 2L/n
fbeat = |f1 - f2|
fo = (v/v+-vs)fs

The Attempt at a Solution

For question 6 i couldn't figure it out..kind of confusing. Question 7 i believe i have to use fn = nv/2L to find the speed...still don't know how to do it
question 8a) fbeat = f1 - f2 therefore, fw - FB = FB + 6 = 220 + 6 = 226 Hz ...is that right? :/

 

[pakman127]

Please show all your work and try add all steps, so i can ask any further questions if i don't understand a step. Please and Thank you! :)

 

[barryj]

No, No. This forum requires YOU to do the work,. or at least give it a good try. Then you will get help.

 

[SteamKing]

What are questions 6 and 7? You stop at question 3.

 

[Nickie]

Hello,

I would be happy to assist you with your questions about waves and sound. Let's take a look at each question and work through the solutions together.

1) To determine the frequency of the water waves, we can use the equation f= 1/T, where f is the frequency and T is the period. We are given the time it takes for 36 wave crests to pass by (4.0 min), so we can first convert this to seconds by multiplying by 60. This gives us 240 seconds for the period (T). Using the equation, we can calculate the frequency (f) as 1/240 = 0.00417 Hz.

2) a) To determine which harmonic this is, we can use the equation fn = nv/2L, where n is the harmonic number, v is the speed of the wave, and L is the length of the string. We are given that there are six nodes, including the ends, so n = 6. The length of the string is 2.0m, and we are given the frequency as 60Hz. Plugging these values into the equation, we get 6 = (6)(v)/2(2.0), which simplifies to v = 360 m/s. Since the speed of the wave is equal to the speed of the wave in the string, we can say that this is the 6th harmonic.

b) To determine the speed of the wave in the string, we can use the equation v = f × λ, where v is the speed, f is the frequency, and λ is the wavelength. We are given the frequency as 60Hz and the length of the string as 2.0m. Using the equation, we get v = (60)(λ). We also know that the wavelength is equal to the length of the string for the fundamental frequency (first harmonic), so we can say that the wavelength is 2.0m. Plugging this into the equation, we get v = (60)(2.0) = 120 m/s.

c) To determine the frequency of the fundamental node, we can use the equation λ-n = 2L/n, where λ is the wavelength, n is the harmonic number, and L is the length of the string. We are given the length of the string as 2.0m and the harmonic