General Properties of Waves Worked ExamplesIGCSE Physics 0625

The graph shows a transverse wave on a rope at one instant. Four distances are marked P, Q, R and S.

(a) State which arrow shows the amplitude and which shows the wavelength.

(b) Use the graph to find the amplitude and the wavelength.

(c) The frequency of the wave is $5.0\text{ Hz}$. Calculate the speed of the wave.

A student moves the end of a stretched spring backwards and forwards to send a wave along it. The diagram shows the spring at one instant.

(a) Describe what is meant by a longitudinal wave.

(b) Name the regions labelled X and Y.

(c) Use the diagram to find the wavelength.

(d) The student's hand moves backwards and forwards $2.5$ times each second. Calculate the speed of the wave.

(e) Name one other wave that can be modelled as longitudinal.

A vibrating bar in a ripple tank produces water waves of frequency $8.0\text{ Hz}$ and wavelength $3.0\text{ cm}$. The frequency is increased to $12\text{ Hz}$. The depth of the water does not change.

What is the new wavelength?

A $1.5\text{ cm}$

B $2.0\text{ cm}$

C $3.0\text{ cm}$

D $4.5\text{ cm}$

The diagram shows six straight wavefronts in a ripple tank, seen from above. The distance from the first wavefront to the sixth is $7.5\text{ cm}$. The vibrating bar has a frequency of $12\text{ Hz}$.

(a) Calculate the wavelength.

(b) Calculate the speed of the waves in m/s.

(c) Explain why measuring across several wavefronts gives a more accurate wavelength than measuring between two neighbouring wavefronts.

A referee's whistle produces a sound of frequency $2.2\text{ kHz}$. The speed of sound in air is $340\text{ m/s}$.

(a) Show that the wavelength of the sound in air is about $0.15\text{ m}$.

(b) The same sound passes into water, where its speed is $1500\text{ m/s}$. State what happens to the frequency, and calculate the wavelength in water.

The speed of electromagnetic waves is $3.0 \times 10^8\text{ m/s}$.

(a) A speed camera uses microwaves of frequency $9.4\text{ GHz}$. Calculate their wavelength.

(b) A green laser emits light of wavelength $530\text{ nm}$. Calculate its frequency. Give your answer in standard form to 2 significant figures.

Straight water waves approach a barrier with a gap. The width of the gap is about the same as the wavelength.

(a) Name the process by which the waves spread out after passing through the gap.

(b) Describe the wavefronts you would draw beyond the gap. The diagram shows the completed answer as dashed lines so that you can check your own.

(c) The gap is made five times wider, and the wavelength is unchanged. Describe how the pattern beyond the gap changes.

Sound waves pass through an open doorway $1.2\text{ m}$ wide. The speed of sound is $330\text{ m/s}$.

Which frequency of sound is diffracted the most as it passes through the doorway?

A $3300\text{ Hz}$

B $1100\text{ Hz}$

C $275\text{ Hz}$

D $5500\text{ Hz}$

Sea waves travel towards a harbour wall. A boat is moored in the sheltered water behind the wall, as shown. E is the end of the wall.

(a) Explain how waves can reach the boat even though it is behind the wall.

(b) On one day the waves have a long wavelength; on another day they have a short wavelength. State on which day the boat will rock more. Explain your answer.

(c) State what happens to the wavelength of the waves as they bend round the end of the wall.

In a ripple tank, a glass plate makes one region of the water shallower. Straight waves of frequency $8.0\text{ Hz}$ cross the boundary at an angle, as shown. The wavelength is $2.0\text{ cm}$ in the deep water and $1.2\text{ cm}$ in the shallow water.

(a) Name the effect shown and state its cause.

(b) State which quantity is the same in both regions.

(c) Calculate the speed of the waves in each region.

(d) Describe how the direction of the waves changes as they cross into the shallow water.

Graph 1 shows the displacement of a wave on a string against distance at one instant. Graph 2 shows the displacement of one point on the string against time.

(a) Find the amplitude and the wavelength.

(b) Find the period and the frequency.

(c) Calculate the speed of the wave.

(d) How far does the wave travel in $5.0\text{ s}$?

A scale drawing shows seven parallel wavefronts of a beam of light. On the drawing, the distance from the first wavefront to the seventh is $14.4\text{ cm}$. The scale of the drawing is $1.0\text{ cm}$ represents $2.5 \times 10^{-7}\text{ m}$.

The speed of light in air is $3.0 \times 10^8\text{ m/s}$.

(a) Determine the wavelength of the light.

(b) Calculate the frequency of the light.

(c) The light enters glass, where its speed is $2.0 \times 10^8\text{ m/s}$. Calculate its wavelength in the glass.