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

the initial frequency is 445Hz

Explanation:

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

The expression for frequency beat is

is the final frequency

is the initial frequency

The expression frequency in term of length is

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

find the sum of the two horizontal vectors and the sum of the two vertical vectors

isoceles right angled triangle

pythagoras' theorem

square root (-5^2+9^2)

square root (25+81)

square root (106)

angle is tan^-1(9/5)

neg x, pos y