Can you please answer both questions A certain sonar is cap

Can you please answer both questions ;)

A certain sonar is capable of echo-ranging at a frequency of 30 kHz to a maximum detection range of 3,000 m on a given submarine target. If the source level of the transducer is increased by 20 dB, what will be the new maximum detection range of the same submarine target? If the transmitted frequency is lowered to 15 kHz, without changing the physical dimensions of the transducer or its acoustic output in watts from that leading to a 3,000 m detection range, what will be the new maximum detection range?

Solution

Ans (i)\'

In underwater acoustics, the convenient term for measurrement is SPL i.e sound pressure

level. SPl s measured in logarithmic (dB) scale.

SPL=10 log(I)---(1)

and I is proportional to the square of R i.e R².

Now the sonar equation states

SL- 2TL+ TS -(NL-DI) = DT ---(1)

SL= source level

TL= transmission loss

TS= target strength

Nl= Noise level

Di =directivity index

DT= detection threshold

we find, if the intensity of the transducer is incresed by a factor of x, range increased by

\\sqrt{x}.

Now in this case, the increament is 20dB. Hence, the factor by which the intensity is

increased is= 10^ (20/10) = 10^2=100 (as it follows log scale)

Hence, the range will be increased by a factor of |sqrt{100)=10.

Hence, the new range will be 3000m X 10=30,000m

Ans b

Here f=125 khz

In sea-water, acoustic absorbption is frequency dependent, lower frequncies reach longer.

The dependence is almost linear.
hence by reducing the frequency by 1/2 , the range is expected to double

if other parameters are kept constant.