The distance between consecutive nodes or antinodes in a sound wave is equal to half the wavelength (λ/2). In this case, the distance between the wall and the antinode is 1 m.
We can use the formula for the wave speed (v) to find the wavelength (λ) of the sound wave: v = fλ
Where: v = wave speed (320 m/s) f = frequency (unknown) λ = wavelength
Since we know the distance between the wall and the antinode is equal to half the wavelength (1 m = λ/2), we can solve for the wavelength:
λ/2 = 1 m
Rearranging the equation, we find:
λ = 2 m
Now, we can substitute the values into the wave speed formula to find the frequency:
v = fλ
320 m/s = f × 2 m
Dividing both sides of the equation by 2 m, we get:
f = 320 m/s / 2 m
f = 160 Hz
Therefore, the frequency of the sound wave at the point 1 m away from the wall is 160 Hz.