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Sound waves travel at 350 m/s through a warm air and at 3500 m/s through brass. The wavelength of a 700 Hz acoustic wave as it enters brass from warm air [2011]
  • a)
    decreases by a factor 10
  • b)
    increases by a factor 20
  • c)
    increases by a factor 10
  • d)
    decreases by a factor 20
Correct answer is option 'C'. Can you explain this answer?
Verified Answer
Sound waves travel at 350 m/s through a warm air and at 3500 m/s throu...
We have, v = nλ
⇒ v ∝ λ (as n remains constant) Thus, as v in creases 1 0 times, λ also increases 10 times.
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Most Upvoted Answer
Sound waves travel at 350 m/s through a warm air and at 3500 m/s throu...
Explanation:
The speed of sound in a medium is given by the formula:
\[
v = f\lambda
\]
Where:
- \(v\) = speed of sound
- \(f\) = frequency of the wave
- \(\lambda\) = wavelength of the wave
Given:
- Speed of sound in warm air (\(v_{warm}\)) = 350 m/s
- Speed of sound in brass (\(v_{brass}\)) = 3500 m/s
- Frequency of the wave (\(f\)) = 700 Hz

Calculating the wavelength in warm air:
Using the formula \(v = f\lambda\), we can calculate the wavelength in warm air (\(\lambda_{warm}\)):
\[
350 = 700 \times \lambda_{warm}
\]
\[
\lambda_{warm} = \frac{350}{700} = 0.5 m
\]

Calculating the wavelength in brass:
Using the formula \(v = f\lambda\), we can calculate the wavelength in brass (\(\lambda_{brass}\)):
\[
3500 = 700 \times \lambda_{brass}
\]
\[
\lambda_{brass} = \frac{3500}{700} = 5 m
\]

Comparing the wavelengths:
The ratio of the wavelength in brass to the wavelength in warm air is:
\[
\frac{\lambda_{brass}}{\lambda_{warm}} = \frac{5}{0.5} = 10
\]
Therefore, the wavelength of the 700 Hz acoustic wave as it enters brass from warm air increases by a factor of 10. Hence, the correct answer is option 'c) increases by a factor 10'.
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