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
Related Physics A Level answers
All answers ▸Two immobile point charges Q1 and Q2 of values +q and +3q respectively are some distance apart. Q3, with value +2q is placed between them and does not move. What is the ratio of the distance between Q3 and Q2 to the distance between Q1 and Q3?
A box initially at rest is on a plank, of length 5m, that is elevated at an angle such that tan(a)=3/4. When it reaches the end of the plank it has velocity 5ms^-1. Calculate the average frictional force on the box.
How can we explain the standing waves on a string?
Why does a body engaged in uniform circular motion do no work?