Read the following case and answer the questions given below:
A student investigates how the temperature of air affects the speed of sound. The student records the following values:
| Temperature of air | Speed of sound |
|---|---|
| \(0^{\circ}C\) | \(331\ ms^{-1}\) |
| \(15^{\circ}C\) | \(340\ ms^{-1}\) |
| \(22^{\circ}C\) | \(344\ ms^{-1}\) |
The student observes that the speed of sound changes with temperature. The student then uses the relation
\(v=\lambda \nu\)
to think about how wavelength and frequency may be affected when the speed changes.
1. What conclusion can the student draw from the investigation about the effect of temperature on the speed of sound in air? Explain using the values in the table.
The data shows that the . At \(0^{\circ}C\), the speed of sound is \(331\ ms^{-1}\), while at \(15^{\circ}C\) it increases to \(340\ ms^{-1}\). At \(22^{\circ}C\), it further increases to \(344\ ms^{-1}\).
2. Compare the speed of sound at \(0^\circ C\) and \(22^\circ C\). Calculate by how much the speed changes.
From the table:
\(v_{0^{\circ}C}=331\ ms^{-1}\)
and
\(v_{22^{\circ}C}=344\ ms^{-1}\)
Therefore, the speed of sound increases by when the temperature changes from \(0^\circ C\) to \(22^\circ C\), according to the given data.
3. The student now considers a sound wave whose frequency remains constant while the speed of sound changes with temperature. Using \(v=\lambda\nu\), explain what happens to its wavelength when the speed increases.
If the , the wavelength depends directly on the speed. Therefore, when the speed of sound increases with temperature,
4. A student says, “The speed of sound is higher at \(22^\circ C\), so the frequency of every sound must also be higher at \(22^\circ C\).” Is this conclusion supported by the investigation? Explain.
. The investigation provides data about the , but it does not provide evidence that the frequency of every sound source changes with temperature. The relationship
\(v=\nu \lambda\)
shows that speed, wavelength and frequency are related, but a change in speed alone does not allow us to conclude that frequency must change in a particular way. Therefore, the student's conclusion is .
5. The speed of sound at \(15^\circ C\) is \(340\,m\,s^{-1}\). If a sound wave has a frequency of \(340\,Hz\) at this temperature, calculate its wavelength.
The wavelength of the sound is \(m\)