Two identical mandolin strings under 200 n of tension are sounding tones with frequencies of 590 hz. the peg of one string slips slightly, and the tension in it drops to 192 n. how many beats per second are heard?

To solve this problem it is necessary to apply the concepts related to frequency and vibration of strings. Mathematically the frequency can be expressed as

Then the relation between two different frequencies with same wavelength would be

The beat frequency heard when the two strings are sounded simultaneously is

We have the velocity of the transverse waves in stretched string as

And,

Therefore the relation between the two is,

Finally substituting this value at the frequency beat equation we have

Therefore the beats per second are 11.92Hz

given data:

determine the horse power (h.p) = ?

force applied to move the box(f) = 10 pounds,

box lifted from a distance         (d) = 3 feet

time taken to lift                         (t) = 10 sec,

the horse power is defined as amount of work required to move a load. the horse power is equal to 550 foot-pound per second

                  1 h.p   = 550 foot-pound/second

it can also be defined as the the load that need to be move a body for certain distance in a certain amount of time.

mathematically,

                      h.p = (force × distance)/ time

                            = (10 × 3)/ 10

                            = 30/10

                            = 3 foot -pound/sec

hence, the horse power is needed to move the box is 3 foot-pound/second

important note: 1 h.p = 550 foot-pound/second = 746 watts