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:
[tex]\lambda=\frac{v}{f}[/tex]
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:
[tex]\begin{gathered} v=331*\sqrt{1+\frac{0}{273}} \\ \\ v=331*\sqrt{1} \\ \\ v=331\text{ m/s} \end{gathered}[/tex]
Now, to find the wavelength, input the values into the formula:
[tex]\begin{gathered} \lambda=\frac{v}{f} \\ \\ \lambda=\frac{331}{20000} \\ \\ \lambda=0.01655\text{ m}\approx16.55\text{ mm} \end{gathered}[/tex]
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:
[tex]\begin{gathered} v=331*\sqrt{1+\frac{40}{273}} \\ \\ v=331*\sqrt{1.1465} \\ \\ v=331*1.0708 \\ \\ v=354.42\text{ m/s} \end{gathered}[/tex]
Hence, to find the wavelength, we have:
[tex]\begin{gathered} \lambda=\frac{v}{f} \\ \\ \lambda=\frac{354.42}{20000} \\ \\ \lambda=0.01772\text{ m}\approx17.72\text{ mm} \end{gathered}[/tex]
The wavelength on a day the temperature is 40 C is 17.72 mm.
ANSWER:
• (a). 16.55 mm
• (,b). 17.72 mm.
