Sound waves travel at $350 ext{ m/s}$ through warm air and at $3500 ext{ m/s}$ through brass. The waveleng

Question

Sound waves travel at $350 	ext{ m/s}$ through warm air and at $3500 	ext{ m/s}$ through brass. The wavelength of a $700 	ext{ Hz}$ acoustic wave as it enters brass from warm air:

Accepted Answer

1. **Identify the Constant Property:** When a wave passes from one medium to another (e.g., from air to brass), its frequency ($f$) remains constant.
2. **Relate Wavelength and Speed:** The speed of a wave is given by the formula $v = f\lambda$. Since the frequency $f$ is constant, the wavelength $\lambda$ is directly proportional to the wave speed $v$ (i.e., $\lambda \propto v$).
3. **Calculate the Ratio:** We can find the change in wavelength by taking the ratio of the speeds in the two media:
   $$\frac{\lambda_{	ext{brass}}}{\lambda_{	ext{air}}} = \frac{v_{	ext{brass}}}{v_{	ext{air}}}$$
   $$\frac{\lambda_{	ext{brass}}}{\lambda_{	ext{air}}} = \frac{3500 	ext{ m/s}}{350 	ext{ m/s}} = 10$$
4. **Conclusion:** The wavelength in brass is 10 times the wavelength in air. Therefore, the wavelength increases by a factor of 10.

Step-by-Step Solution

Practice All PHYSICS Questions