Question 61: Waves

Question

Column I shows four systems, each of the same length L, for producing standing waves. The lowest possible natural frequency of a system is called its fundamental frequency, whose wavelength is denoted as $$\lambda$$f. Match each system with statements given in Column II describing the nature and wavelength of the standing waves :

Accepted Answer

(1) For a pipe closed at one end, we have
$${{{\lambda _f}} \over 4} = L$$ or $${\lambda _f} = 4L$$
Therefore, the sound waves are longitudinal.
(2) For a pipe open at both ends, we have
$${{{\lambda _f}} \over 2} = L$$ or $${\lambda _f} = 2L$$
Therefore, the sound waves are longitudinal.
(3) For a stretched wire clamped at both ends, we have
$${{{\lambda _f}} \over 2} = L$$
Vibration on the string is transverse.
(4) For a stretched wire clamped at both ends and at mid-point, we have
$${{{\lambda _f}} \over 2} = {L \over 2} \Rightarrow {\lambda _f} = L$$
Therefore, the vibration on the string is transverse.

Answer

(A)$$	o$$(T); (B)$$	o$$(P), (S); (C)$$	o$$(Q), (S); (D)$$	o$$(Q)

Answer

(A)$$	o$$(P), (T); (B)$$	o$$(P); (C)$$	o$$(Q), (S); (D)$$	o$$(Q)

Answer

(A)$$	o$$(P); (B)$$	o$$(P), (S); (C)$$	o$$(Q); (D)$$	o$$(Q), (R)

Answer

(A)$$	o$$(P), (T); (B)$$	o$$(P), (S); (C)$$	o$$(Q), (S); (D)$$	o$$(Q), (R)

Waves

Choose the correct answer: