To determine the frequency of string
A, we start with the following information:
Initial beat frequency is 4 beats per second.
Frequency of string
B,fB=480Hz.
The relation for beat frequency:
|fA−fB|=4.
Given that the tension on string
A is increased, the frequency of
A will increase, leading to an increase in the beat frequency. The new beat frequency becomes 7 beats per second.
The vibration frequency of a string is determined by the formula:
f=‌⋅√‌Where:
n is the mode of vibration.
L is the length of the string.
T is the tension in the string.
µ is the linear mass density.
Since the tension in string
A is increased, we know the frequency of
A increases. Consequently, the following must be true for the beat frequency to increase:
fA−fB=4‌‌‌ or ‌‌‌fB−fA=4However, since the frequency of
A increases and the beat frequency becomes 7, it implies that:
fA−fB=7Given:
Initially,
fA−480=4, thus
fA=484Hz.
Therefore, as
fA increases past 480 Hz and still satisfies the condition where the beat frequency becomes 7 , this confirms that initially:
fA=484Hz