Question

In addition to producing images, ultrasound can be used to heat tissues of the body for therapeutic purposes. An emitter is placed against the surface of the skin; the amplitude of the ultrasound wave at this point is quite large. When a sound wave hits the boundary between soft tissue and bone, most of the energy is reflected. The boundary acts like the closed end of a tube, which can lead to standing waves. Suppose 0.70 MHz ultrasound is directed through a layer of tissue with a bone 0.55 cm below the surface. Will standing waves be created? Explain.

Answer 1

Answer:

The answer is Yes, the standing wave length with 5 anti-nodes  will be created

Explanation:

To answer this question, we recall the frequencies of standing wave modes in a closed - closed tube of length (L).

The formula will now be:

                    Fₙ =  n ( v/2L)

Where n = n is equal to the number of anti-nodes

and

lambda = 2L/n for standing waves in a closed tube where n is equal to the number of nodes

Now assuming the nodes are :

Where n = 1, 2, 3, 4, 5, ............

Now, we try to make "n" the subject of formula

Fₙ =  n ( v/2L)

So therefore, the number of nodes produced will be

n = 2L Fₙ / v

2 x 0.55 x  10⁻² x 0.7 x 10⁶  / 1540

Calculating the above further, we arrive at = 5.

Now to answer the question,

The answer is Yes, the standing wave length with 5 anti-nodes  will be created