IIT JEE Advanced 2011 Paper 2

(A)→(P), (T) For a pipe closed at one end, we have $\frac{\lambda_f}{4}$ = L or $\lambda_f$ = 4L Therefore, the sound waves are longitudinal. (B)→(P), (S) For a pipe open at both ends, we have $\frac{\lambda_f}{2}$ = L or $\lambda_f$ = 2L Therefore, the sound waves are longitudinal. (C)→(Q), (S) For a stretched wire clamped at both ends, we have $\lambda_f$/2 = L Vibration on the string is transverse. (D)→(Q), (R) For a stretched wire clamped at both ends and at mid-point, we have $\frac{\lambda_f}{2}$ = $\frac{L}{2}$ ⇒ $\lambda_f$ = L Therefore, the vibration on the string is transverse.