Question

29a)A violin string is set in vibration at a frequency of 440Hz. How many vibrations does it make while its sound travels 200m if the temperature is 25C

29b)A wire with a linear mass density of 2.5x10^-3 kg/m is under 35N of tension. If the wire is plucked what is the frequency of the wave on the wire if its wavelength is 2m

Answer 1

29a) we know,

speed of sound, v = vo + 0.6*T

= 331 + 0.6*25

= 346 m/s

time taken to travel, t = d/v

= 200/346

= 0.578 s

no of vibrations made during this time = t/Time period

= t/(1/f)

= t*f

= 0.578*440

= 254 <<<<<<<<<-----------------Answer

29b)

given
mue = 2.5*10^-3 kg/m
T = 35 N
lamda = 2 m
speed of wave on the string, v = sqrt(T/mue)

= sqrt(35/(2.5*10^-3))

= 118.3 m/s

now use, v = lamda*f

===> f = v/lamda

= 118.3/2

= 59 Hz <<<<<<<<<------------Answer