Question

In each of the four situations of Column-I a stretched string or an organ pipe is given along with required data. In case of strings the tension in string is 102.4 N and the mass per unit length of string is 1 g/m. Speed of sound in air is 320 m/s. Neglect and corrections. The frequencies of resonance are given in column II. Match each situation in column-I with the possible resonance frequencies given in column-II.
Column-I Column-II
A) String fixed at both end P) 320 Hz
B) String fixed at one end and free at other end Q) 480 Hz
C) Open organ pipe R) 640 Hz
D) Closed organ pipe S) 800 Hz

• A. A-PR, B-QS, C-PR, D-QS
• B. A-PS, B-QR, C-PQ, D-QS
• C. A-QR, B-PQ, C-QS, D-RS
• D. A-PR, B-QR, C-SR, D-RP

Answer 1

The correct option is A A-PR, B-QS, C-PR, D-QS

Speed of string wave is $\sqrt{\frac{T}{\mu }}=\sqrt{\frac{102.4}{0.00L}}=320m/s$

$\mu =0.001kg/m$

For case $A:$ String fixed at both end.

If $\frac{v}{4l}=320$ Then next would be $640$ because only even multiplies of base frequency is present.

So, $A\to PR$

Case $B:$ String open at one end.

If $\frac{3v}{4l}=480$ Then next would be $800$ because only odd harmonics are present.

Now, case $C$ is similar as case $A$.

and $D$ is similar as $B$.