Explain how the speed of sound in air depends on temperature. A source emits sound of frequency $300,\text{Hz}$. If the ambient temperature changes from $20^{\circ }\text{C}$ to $30^{\circ }\text{C}$, calculate the change in frequency observed by a stationary observer, assuming the source frequency remains unchanged. Use $v=331+0.6T$ where $T$ is in degrees Celsius.

Step-by-step solution

1. 1. Compute speed of sound at $20^{\circ }\text{C}$: $v_{20}=331+0.6\times 20=343,\text{m/s}$.
2. 2. Compute speed at $30^{\circ }\text{C}$: $v_{30}=331+0.6\times 30=349,\text{m/s}$.
3. 3. The source frequency $f_s$ is fixed at $300,\text{Hz}$; it does not depend on the medium or temperature.
4. 4. For a stationary observer, the observed frequency $f_o$ equals the source frequency $f_s$ regardless of the speed of sound.
5. 5. Therefore, the observed frequency remains $300,\text{Hz}$ at both temperatures; the change is $0,\text{Hz}$.

Concept tested: Temperature effect on speed of sound, frequency invariance

Published 10 October 2026 · How this solution was prepared and checked