A sound wave travels from a region of air at $20^{\circ }\text{C}$ into a region at $40^{\circ }\text{C}$. What is the ratio of the wavelengths ($\lambda _{40}/\lambda _{20}$), if the frequency remains constant?

Question

A pipe open at both ends has a fundamental frequency $f$ in air. The pipe is now dipped vertically in water drum to half of its length. The fundamental frequency of the air column is now equal to:

Answer 1

Step 1: Speed ratio
$\frac{v_{40}}{v_{20}}=\sqrt{\frac{T_{40}}{T_{20}}}=\sqrt{\frac{313}{293}}$.

Step 2: Frequency fixed
$\lambda=\frac{v}{f}$, so the wavelength ratio equals the speed ratio.

Step 3: Why the other options fail
Using $\frac{40}{20}$ or $\sqrt{\frac{40}{20}}$ uses Celsius values, but the law needs absolute temperature. The option $\frac{313}{293}$ forgets the square root.

Final Answer:
The ratio is the square root of 313/293. \[ \boxed{\text{(A) }\sqrt{\dfrac{313}{293}}} \]

A sound wave travels from a region of air at \(20^{\circ }\text{C}\) into a region at \(40^{\circ }\text{C}\). What is the ratio of the wavelengths (\(\lambda _{40}/\lambda _{20}\)), if the frequency remains constant?

Show Hint

The Correct Option is A

Solution and Explanation

Top Questions on Sound Wave

Questions Asked in MHT CET exam