Question

A violin player hears 5 beats per second when she plays a note and sounds a 440 Hz tuning fork. After turning the tuning knob to tighten the string, she hears 3 beats per second against the tuning fork. Was her initial frequency 435 Hz or 445 Hz

Answer 1

Answer: 445 Hz

Explanation:

The frequencies differ by 5 Hz. This is because her beats occurs 5 times per second. As she turned the tuning knob, which resulted in a reduction of tension. The decreased speed of wave on the spring also reduces its frequency.

In all, the original frequency has to be higher than 440 Hz. And since she heard 5 beats per second before turning the knob. Her original frequency is 440 Hz + 5 Hz = 445 Hz

Answer 2

Answer:

the initial frequency is 445Hz

Explanation:

The number of beat produce is equal to the difference in frequencies

The expression for frequency beat is

$f_{beat} = |f_2 - f_1|$

$f_2$ is the final frequency

$f_1$ is the initial frequency

The expression frequency in term of length is

$f = \frac{v}{2L}$

where,

f is the frequency

v is the speed

L is the length

From the above ,it is clear that frequency is directly proportional to length,

after the length of the trumpet increase , the frequency produced by it decrease , since the beat frequency increases. If the initial frequency is 435Hz , the frequency produced by the trumpet is less than the value of 5beat/sec

Hence, there is no chance to produce 3 beat/sec when it sound is 440Hz ,

that means the number of beat produced should be greater than 5beat/sec.

If the initial frequency is 445Hz , the frequency produced b the trumpet is less than value of 445Hz. Thus , there will be a chance to produce 3beat/sec when it turn into tuning fork of 440Hz

Therefore, the initial frequency is 445Hz