Pitch Change with Temperature – Rankers Physics
Topic: Waves
Subtopic: Sound Wave and its Characteristics

Pitch Change with Temperature

Assertion (A): The pitch of wind instruments rises and that of string instruments falls as an orchestra warms up.
Reason (R): When temperature rises, speed of sound in air increases but speed of wave in a string fixed at both ends decreases.
 
Both (A) & (R) are true and the (R) is the correct explanation of the (A)
Both (A) & (R) are true but the (R) is not the correct explanation of the (A)
(A) is true but (R) is false
Both (A) and (R) are false

Solution:

For wind instruments, pitch \( f \) is proportional to the speed of sound in air \( v_{\text{air}} propto \sqrt{T_{\text{temp}}} \). As temperature rises, \( v_{\text{air}} \) increases, so pitch rises. For string instruments, \( f propto v_{\text{string}} = \sqrt{T_{\text{tension}}/\mu} \). As temperature rises, the string expands, reducing tension \( T_{\text{tension}} \), so \( v_{\text{string}} \) decreases and pitch falls. Reason R accurately explains this behavior for both cases.

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