What are the frequency and the wavelength of the sound waves produced in water at 0 degrees C?

Question

So, this is a physics question I'm having some serious trouble with, help would be appreciated. Here's the question in all its detail:

A vibrating 400Hz tuning fork is placed in pure distilled water.
a) What are the frequency and the wavelength (in metres) of the sound waves produced within the water at 0 degrees C?
b) What would be the frequency and the wavelength in the adjacent air, if the sounds waves moved from the water into the air at 0 degrees C?

That's the question, I got the second half already...I think, but I can't figure out a) at all.

The equations we have are :
frequency = cycles/time
Period = time/cycles
Speed = frequency x wavelength
Speed = distance/time
Speed of Sound in Air = (332+(0.6xTemperature))

I have the answers in my text if anyone could get anywhere backwards.

Any help would be much appreciated.

Extra Details : The frequency stays 400Hz, in both mediums.
The wavelength in b) is 0.83 metres, and the wavelength in a) according to the text book which has been wrong before is 3.83 metres.

Answer 1

I can't understand this question. Is the tuning fork totally immersed in the water? Then its frequency will be radically changed and the oscillation highly damped due to the water's inertia, relative incompressibility and resistance to motion. There's no way to compute its frequency without having a lot more information (at a minimum, details about the mass, size & shape of the tuning fork) and the calculation would be complex and difficult.
OK, so let's suppose its vibration is coupled to the water without beng immersed. Then it oscillates at 400 Hz, and this is the frequency of the sound in the water. The wavelength is then a trivial calculation.
Surely I'm missing something. I think you should provide the answer (via the "add details" option) and see what people think then.
EDIT: Since you added the answers, there's no disagreement on the frequency. The wavelength in any medium is the speed divided by the frequency, so there's no disagreement on the wavelength in air. However, the speed of sound in water is a parameter that many physicists have attempted to formulate. The generally agreed value at 0C is about 1430 m/s. Using the web page given below and the Marszak interactive calculator available there, I get 1402.385 m/s, which yields a wavelength of 1402.385/400 = 3.505963 m. (The other calculators on that page all agreed on the speed within 0.003 m/s.) The textbook's answer of 3.83 m implies a speed of 1532 m/s, which the Marszak calculator equates to a temperature of 42C! I think the textbook's author(s) have some explaining to do.

Answer 2

Property of water is just the velocity of vibrations in it. Whatever frequency you make its particles vibrate waves with wavelength equal to velocity divided by frequency will be produced in infinite expanse of water. If it is limited expanse then waves of wavelength which fit in full measure of half wavelengths can be produced so that there is node always at the end of the water where it touches the container. then various modes or frequencies will be produced to be obtained by dividing velocity by wavelength. I have told you physics now you evaluate and find the answers or put some related query.

Answer 3

Wavelength in this case is in units of meter (m). Divide the speed by the wavelength and include all units and you get (330*m/s)/(0.3*m)= (330/0.3)*m/(m*s) The units of this result have meters in both numerator and denominator, so they cancel each other out to 1/1 so they disappear, leaving (330/0.3)/s= 1100/s. Frequency also has units of 1/s which is also called Hz (hertz). So 1100/s = 1100Hz. -- Regards, John Popelish