You blow a whistle of frequency 942 Hz, as you move towards a wall.

The frequency of beats you hear from the whistle and the reflected sound is 7 beats/s.

In m/s and to two significant figures, how fast are you moving towards the wall?

942+7= 949

949 = f (340+v/340)

f= 942 (340/340-v)

Isolate for frequency

949/942 = (340+v/340-v)

v= 1.26m/s (speed at which a whistler is moving)

To find the speed at which you are moving towards the wall, we need to use the formula for the Doppler effect:

v = (f * λ) / (f0 - f)

where:
v = speed of the source or observer relative to the medium (in this case, your speed towards the wall)
f = frequency of the source or observer (in this case, the frequency of the whistle)
λ = wavelength of the sound wave
f0 = frequency of the sound wave at rest or unaffected by the Doppler effect (in this case, the frequency of the whistle when not moving)

First, we need to find the wavelength of the sound wave. We can use the equation:

v = λf

where:
v = speed of sound in air (approximately 343 m/s)
λ = wavelength of the sound wave
f = frequency of the sound wave

We can rearrange the equation to solve for λ:

λ = v / f

Substituting the values, we have:

λ = 343 / 942 ≈ 0.364 m

Next, let's calculate the frequency of the whistle when not moving (f0). Since the frequency of beats is given as 7 beats/s and it is the difference between the frequency of the whistle and the reflected sound, we have:

f - f0 = 7

Solving for f0, we get:

f0 = f - 7

Now we substitute the values into the Doppler effect formula:

v = (f * λ) / (f0 - f)

v = (942 * 0.364) / (942 - (942 - 7))

Simplifying further:

v = (342.408) / 7 ≈ 48.915 m/s

Therefore, you are moving towards the wall at a speed of approximately 48.915 m/s.