Sound waves travel through air at a speed of 330 m/s. A whistle blast at a frequency of about 1.0 kHz lasts for 2.0 s. (a) Over what distance in space does the "wave train" representing the sound extend? (b) What is the wavelength of the sound? (c) Estimate the precision with which an observer could measure the wavelength. (d) Estimate the precision with which an observer could measure the frequency.

a)   x = 660 m , b)    λ = 0.330 m , c) precision  is 0.1 cm , d)    Δf= n Δt/ t²

Explanation:

a) the speed of sound is constant, therefore we can use the relation of motion to inform the distance that the sound extends is

        v = x / t

         x = v t

         x = 330 2

         x = 660 m

b) the speed of sound is

          v = λ f

          λ = v / f

          λ = 330/1000

          λ = 0.330 m

c) a measuring tape must be used to measure the wavelength, the precision  is 0.1 cm

.d) frequency measurement is more delicate, a stopwatch should be used to measure a certain number of oscillations, and hence calculate the frequency

         .f = n / t

Therefore, if we assume that there is no error in the number of oscillations, the pressure is given by the appreciation of the stopwatch, which is maximum 0.01 s

           Δf / f = Δt / t

           Δf = Δt /t   f

           Δf= n Δt/ t²