Question

It was the same sound as produced on a hot day of 40°C what is the wave length in millimeters of the wave in the water temperature

Answer 1

Given:

Frequency, f = 20 kHz.

Speed of sound in air, v = 331 m/s

Let's find the wavelength for the following:

• (a). When the temperature is 0 degrees Celsius.

To find the wavelength, apply the formula:

`\lambda=(v)/(f)`

Where:

v is the speed

f is the frequency in Hz = 20 x 1000 = 20000 Hz.

To find the speed of sound on a day with 0 C, we have:

`\begin{gathered} v=331*\sqrt{1+(0)/(273)} \\ \\ v=331*√(1) \\ \\ v=331\text{ m/s} \end{gathered}`

Now, to find the wavelength, input the values into the formula:

`\begin{gathered} \lambda=(v)/(f) \\ \\ \lambda=(331)/(20000) \\ \\ \lambda=0.01655\text{ m}\approx16.55\text{ mm} \end{gathered}`

The wavelength when the temperature is 0 C is 16.55 mm.

• (b). Wavelength when the temperature is 40 degrees Celsius.

The speed, v, on a day when the temperature is 40 C will be:

`\begin{gathered} v=331*\sqrt{1+(40)/(273)} \\ \\ v=331*√(1.1465) \\ \\ v=331*1.0708 \\ \\ v=354.42\text{ m/s} \end{gathered}`

Hence, to find the wavelength, we have:

`\begin{gathered} \lambda=(v)/(f) \\ \\ \lambda=(354.42)/(20000) \\ \\ \lambda=0.01772\text{ m}\approx17.72\text{ mm} \end{gathered}`

The wavelength on a day the temperature is 40 C is 17.72 mm.

ANSWER:

• (a). 16.55 mm

• (,b). 17.72 mm.