On a keyboard, you strike a note having a frequency of 256 Hz. (a) Show that the period of one vibration of this tone is 0.00391s. (b) As the sound leaves the instrument at a speed of 340 m/s, show that its wavelength in air is 1.33m.
period = 1/frequency.
speed = frequency x wavelength
To solve this problem, we can use the formulas relating frequency, period, velocity, and wavelength.
(a) We know that the frequency is 256 Hz. The formula relating frequency and period is:
Period (T) = 1 / Frequency (f)
Plugging in the frequency:
T = 1 / 256 Hz
= 0.00391 s
Therefore, the period of one vibration of this tone is 0.00391s.
(b) To find the wavelength, we can use the formula:
Wavelength (λ) = Velocity (v) / Frequency (f)
Plugging in the values:
λ = 340 m/s / 256 Hz
= 1.33 m
Hence, the wavelength of the sound in air is 1.33m.
To find the period of one vibration of the tone, we can use the formula:
Period (T) = 1 / Frequency (f)
Given that the frequency (f) is 256 Hz, we can substitute it into the formula:
T = 1 / 256 Hz
T ≈ 0.00391s
Therefore, the period of one vibration of this tone is approximately 0.00391 seconds.
To find the wavelength of the sound in air, we can use the formula:
Wavelength (λ) = Speed of Sound (v) / Frequency (f)
Given that the speed of sound (v) is 340 m/s and the frequency (f) is 256 Hz, we can substitute the values into the formula:
λ = 340 m/s / 256 Hz
λ ≈ 1.33 m
Therefore, the wavelength of the sound in air is approximately 1.33 meters.