If the highest frequency a song is 10 kHz and it is encoded at 16 bits per sample what is the minimum number of bytes needed to encode the 3 minute song?

The key to this question is to remember the Nyquist rate of a signal. This is the lowest sample rate which can be used for a signal without losing valid frequencies or gaining incorrect frequencies. This is equal to twice the highest frequency.

Therefore the sample rate needs to be 20 kHz. Since there are 16 bits per sample the number of bits per second is 16 multiplied by 20 000 which is 320 000 bits per second.

To calculate the number of bits in 3 minutes we need to multiply 320 000 by the number of seconds in 3 minutes. Which gives:
320 000 x 3 x 60 = 57 600 000 bits 

Remember to divide by 8 to get it in bytes, since there are 8 bits in a byte. This finally gives:
57 600 000/8 = 7 200 000 bytes = 7.2 Megabytes

DM
Answered by David M. Physics tutor

6147 Views

See similar Physics A Level tutors

Related Physics A Level answers

All answers ▸

Explain, using appropriate laws of motion, why the air exerts a force on the engine in the forward direction.


Calculate the length of a 120m (as measured by the astronaut) spaceship travelling at 0.85c as measured by a stationary observer


A block of ice slides down the full height from one side of a 1m high bowl and up the other side. Assuming frictionless motion and taking g as 9.81ms-2, find the speed of the block at the bottom of the bowl and the height it reaches on the the other side.


I do 400J of work compressing a gas, but I maintain the same temperature. What is the delta U, Q and W in this case?


We're here to help

contact us iconContact ustelephone icon+44 (0) 203 773 6020
Facebook logoInstagram logoLinkedIn logo

MyTutor is part of the IXL family of brands:

© 2025 by IXL Learning