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numerical problems [4 marks]
30. 2076 set b q. no. 111 a wire whose mass per unit length
10^-3 kg/m is stretched by a load of 4 kg over the two bridges
of a sonometer wire 1 m apart. it is struck at its middle point,
what would be the wavelength and frequency of its
fundamental vibration?
ans: 100 hz
60
[4]

λ = 2 m

f = 100 Hz

Explanation:

When struck in the middle an anti-node is formed at the center, So you can derive,

f = frequency of the fundamental mode in producing standing waves

l = resonating length

T = tension of the wire

m = linear density of the wire

(check the attachment)

By substituting,

f = 100 Hz

Wavelength is twice the vibrating  length, its in the section standing waves and using that only the equation is derived.

Imagine what happens when two identical waves in opposite direction superimpose. There will be 3 nodes and two anti-nodes where the distance between two nodes is half the wavelength.

The same case happen here, the transverse sound wave traveling along the wire get reflected by a bridge and bounce back on itself where superposition takes place. So two nodes are at the bridges hence the twice of the distance between bridges is the wavelength of the sound wave.

answer;

d. are made mostly of liquid

explanation;

-the general   composition and structure planets includes; they have a thick gas and liquid layer covering a small,solid core. mostly the gases are hydrogen and helium atmosphere and layers of liquid hydrogen. for instance neptune and uranus are examples of the outer planets, they have a core covered by ice and ammonia.

-neptune's atmosphere is hydrogen and helium with a bit of methane so there is no oxygen to breath and the interior is made up of frozen water and ammonia with a rock and iron core. thus, there is no liquid water or solid surface to survive.

find the sum of the two horizontal vectors and the sum of the two vertical vectors

isoceles right angled triangle