A vibrating 400.0Hz tuning fork is placed in fresh water. What is the frequencyin herbs and the wavelength in meters

(A) within the water at 25c
(B) when the sound waves move into the air at 25c

The frequency does not change (actually it does due to added mass of water but not to first order)

The velocity of sound in water is greater than in air so the wavelength will be greater.

Tair = period in air = 1/400
wavelength in air = Vair * 1/400

Twater = 1/400
wavelength in water = Vwater * 1/400

To determine the frequency and wavelength of a vibrating tuning fork in fresh water, we need to consider the speed of sound in both water and air.

(A) Frequency and wavelength within water at 25°C:
To find the frequency within water, we need to know the speed of sound in water, which is approximately 1482 m/s at 25°C. We can use the equation:

Speed = Frequency x Wavelength

In this case, we want to find the frequency, so we rearrange the equation:

Frequency = Speed / Wavelength

Given that the speed of sound in water is 1482 m/s, we can substitute it into the equation:

Frequency = 1482 m/s / Wavelength

Now, we need to determine the wavelength. The wavelength can be calculated using the equation:

Wavelength = Speed / Frequency

Since the tuning fork's frequency is 400.0 Hz, we can substitute the values into the equation:

Wavelength = 1482 m/s / 400.0 Hz

Calculating the wavelength:

Wavelength = 3.705 m / Hz

So, within water at 25°C, the frequency is 400.0 Hz, and the wavelength is 3.705 m.

(B) Frequency and wavelength when the sound waves move into the air at 25°C:
When the sound waves move from water into the air, the speed of sound changes. In air at 25°C, the speed of sound is approximately 343 m/s.

To find the frequency in air, we can use the same equation as before:

Frequency = Speed / Wavelength

Given that the speed of sound in air is 343 m/s, we can substitute it into the equation:

Frequency = 343 m/s / Wavelength

To find the wavelength, we can rearrange the equation:

Wavelength = Speed / Frequency

Substituting the given frequency (400.0 Hz), we can calculate the wavelength:

Wavelength = 343 m/s / 400.0 Hz

Calculating the wavelength:

Wavelength = 0.8575 m / Hz

So, when the sound waves move into the air at 25°C, the frequency is still 400.0 Hz, but the wavelength becomes 0.8575 m.