stephens and bate formula

mail

Hi I would be grateful if someone could explain this formula . I will have an exam this week and this may come up. I know the 0.0118 and .107 are constants but cant understand the midddle bit, thanks

hivizman

The Stephens and Bate formula is designed to measure the optimal reverberation time for sound in an enclosed space. The reverberation time is defined as the time taken for sound to decay by 60 decibels. Because this time varies according to the frequency of the sound, it is usual to calculate the optimal time at a given frequency, typically 500 Hz (as a comparison, at modern concert pitch, the note middle A is tuned to 440 Hz).

The formula is:

T500 = k[0.0118(3√V) + 0.107]

k is a constant that takes different designated values according to the nature of the sound (4 for speech, 5 for orchestral music, 6 for choral music).

The middle term 3√V is intended to be the cube root of V, where V is the volume of the enclosed space measured in cubic metres.

For example, if you consider a living room 5 x 4 x 3 metres, the volume V will be 60 cubic metres, and the cube root of this is 3.914. If the sound being considered is speech, then the optimal reverberation time will be:

3 x [0.0118 x 3.914 + 0.107] = 0.46 seconds (roughly half a second).

On the other hand, the optimal reverberation time for a large hall used for choral music (the hall being 30 x 20 x 10 metres) would be calculated as follows:

V = 30 x 20 x 10 = 6000 cubic metres. The cube root of 6000 is 18.17, and k = 6, so the formula is:

6 x [0.0118 x 18.17 + 0.107] = 1.92 seconds (roughly two seconds).

The formula can be used for irregularly shaped volumes, not just for rectangular box shapes.

mail

Thanks for the quick reply , that is a great explanation pity you are not my teacher. I am a mature student who left school early so could you explain how I can get the cube root of the number other than that I understand now what you are saying, thanks again for the quick reply.

bnt

If your calculator doesn't have a cube root function, you can also find it by raising the number to the power of 1/3. For example [latex]^3\sqrt{17}= 17^{\frac{1}{3}} = 2.571[/latex]

Capt'n Midnight

or you can get the log of a number (Ln)
divide it by three
and the use (ex) to convert the log back to a number