There aren’t any noise canceling earphones that can be completely soundproof all the time. They work best at canceling out low-frequency sounds such as the hum of the airplane or train you might be riding. They’re not as effecting at higher frequency sounds so if I sudden cry breaks out it will still get through. That being said some are indeed better at it than others are.
Bose is one brand that tends to drop consistent products when it comes to noise canceling headphone options. The QuietComfort 25 (“QC25”) are an update from the QuietComfort 15s. They’re lightweight at 6.9 oz (195.6 g), and last about 35 hours on AAA batteries. The earphones will warn you when they have about seven hours of life left in them, which is a lot more than you can say for that smartphone.
They’re available on Amazon for about $300.